Spatially homogeneous solutions of the Vlasov-Nordstrom-Fokker-Planck system
Journal article, 2014
The Vlasov-Nordstrom-Fokker-Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the spatially-homogeneous system and prove global existence and uniqueness of solutions for the corresponding initial value problem in three momentum dimensions. Additionally, we study the long time asymptotic behavior of the system and prove that even in the absence of friction, solutions possess a non-trivial asymptotic profile. An exact formula for the long time limit of the particle density is derived in the ultra-relativistic case.
Global existence
STEADY-STATES
EXISTENCE
EQUATION
Mathematics
Vlasov-Nordstrom
Spatially homogeneous
BEHAVIOR
Fokker-Planck equation
Ultra-
Author
J. A. A. Felix
Universidad de Granada
Simone Calogero
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
S. Pankavich
Colorado School of Mines
Journal of Differential Equations
0022-0396 (ISSN) 1090-2732 (eISSN)
Vol. 257 10 3700-3729Subject Categories
Mathematics
DOI
10.1016/j.jde.2014.07.006